I think that intelligence is much more environmentally driven rather than genetic, though I don't have any proper references for that. I would argue that, in a properly functioning society, intellectualism, assuming it's strongly tied to wealth, wouldn't really be heritable beyond one generation.

Combating anti-intellectualism as a trend is probably more complicated than just trying to get the existing educated to have more children then the existing uneducated.

> One might argue intellectuals have an obligation to procreate.

They already did and their kids are building the world's largest and most powerful surveillance and propaganda systems at Facebook and Google. Unfortunately the "G" in FAANG does not stand for "Greenpeace".